If it’s shellac Mineral Spirits will NOT work. The stronger commercial strippers ( for Epoxy, Urethane etc. )will work due to their alcohol content. If you use those…READ THE LABEL!
Almost any alcohol, Rubbing(isopropanol), denatured (ethanol) and Wild Turkey 101 will work but the water content will raise the grain, so I’d get a gallon of denatured alcohol from your local big box or hardware store, it will have a low water content. You’ll probably need that much for all the cabinets.
But, first check to see if the finish really is shellac by saturating a rag with whatever alcohol is handy and hold it against the cabinet surface to see if the finish becomes sticky and starts to dissolve.
If after several applications the finish isn’t softening you may have a varnish of some type. In that case you can use any of the commercial strippers.
Remember to wear Nitrile gloves and extinguish any sources of ignition ie. pilot lights etc. and most important safety glasses and forced air ventilation.
Probably easiest to remove the doors and drawers and hardware to be able to work on a horizontal surface out side if possible.
Any way you look at it, this is going to be a messy process.
Are you sure you need to strip? The evenness of color looks excellent and the finish is worn but not awful, so if it is really shellac it might be quite possible to just refresh it. I’d at least try removing the grease and gunk followed by padding on some shellac, just to see. If it looks promising, then keep going with the shellac.